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Implementing a set of microeconomic criteria, we develop price dynamics equations using a function of demand/supply with key symmetry properties. The function of demand/supply can be linear or nonlinear. The type of function determines the…

Mathematical Finance · Quantitative Finance 2019-04-02 Carey Caginalp , Gunduz Caginalp

Stochastic ordering of distributions of random variables may be defined by the relative convexity of the tail functions. This has been extended to higher order stochastic orderings, by iteratively reassigning tail-weights. The actual…

Statistics Theory · Mathematics 2017-03-14 Idir Arab , Paulo Eduardo Oliveira

We propose a novel probabilistic model to facilitate the learning of multivariate tail dependence of multiple financial assets. Our method allows one to construct from known random vectors, e.g., standard normal, sophisticated joint…

Risk Management · Quantitative Finance 2020-01-14 Xing Yan , Qi Wu , Wen Zhang

Existing theory for multivariate extreme values focuses upon characterizations of the distributional tails when all components of a random vector, standardized to identical margins, grow at the same rate. In this paper, we consider the…

Statistics Theory · Mathematics 2013-12-20 J. L. Wadsworth , J. A. Tawn

A decision must often be made between heavy-tailed and Gaussian errors for a regression or a time series model, and the t-distribution is frequently used when it is assumed that the errors are heavy-tailed distributed. The performance of…

Computation · Statistics 2015-05-11 J. Martin van Zyl

We study the long-time behavior of the scaled walker (particle) position associated with decoupled continuous-time random walk which is characterized by superheavy-tailed distribution of waiting times and asymmetric heavy-tailed…

Statistical Mechanics · Physics 2013-02-19 S. I. Denisov , Yu. S. Bystrik , H. Kantz

We extend the construction principle of multivariate phase-type distributions to establish an analytically tractable class of heavy-tailed multivariate random variables whose marginal distributions are of Mittag-Leffler type with arbitrary…

Probability · Mathematics 2020-03-25 Hansjoerg Albrecher , Martin Bladt , Mogens Bladt

Products between phase-type distributed random variables and any independent, positive and continuous random variable are studied. Their asymptotic properties are established, and an expectation-maximization algorithm for their effective…

Probability · Mathematics 2021-11-25 Hansjoerg Albrecher , Martin Bladt , Mogens Bladt , Jorge Yslas

We study the tail behavior of the distribution of the sum of asymptotically independent risks whose marginal distributions belong to the maximal domain of attraction of the Gumbel distribution. We impose conditions on the distribution of…

Probability · Mathematics 2009-06-29 Abhimanyu Mitra , Sidney I. Resnick

We consider the evolution of scale-free networks according to preferential attachment schemes and show the conditions for which the exponent characterizing the degree distribution is bounded by upper and lower values. Our framework is an…

Statistical Finance · Quantitative Finance 2013-01-07 João P. da Cruz , Pedro G. Lind

A discrete version of the Gumbel (Type I) extreme value distribution has been derived by using the general approach of discretization of a continuous distribution. Important distributional and reliability properties have been explored. It…

Statistics Theory · Mathematics 2014-10-29 Subrata Chakraborty , Dhrubajyoti Chakravarty

Statistical description of stochastic dynamics in highly unstable potentials is strongly affected by properties of divergent trajectories, that quickly leave meta-stable regions of the potential landscape and never return. Using ideas from…

Statistical Mechanics · Physics 2019-08-22 Artem Ryabov , Viktor Holubec , Ekaterina Berestneva

In this survey we present an extensive research of the vast literature about the Generalized Lambda Distribution (GLD) and propose a hurdle, or two-way, model whose associated distribution is the GLD in order to meet the demand for a highly…

Applications · Statistics 2019-01-04 Diego Marcondes , Cláudia Peixoto , Ana Carolina Maia

Empirical distributions have their in-sample maxima as natural censoring. We look at the "hidden tail", that is, the part of the distribution in excess of the maximum for a sample size of $n$. Using extreme value theory, we examine the…

Statistical Finance · Quantitative Finance 2020-04-14 Nassim Nicholas Taleb

We propose the test for distinguishing between two classes of distribution tails using only the largest order statistics of the sample and state its consistency. We do not assume belonging the corresponding distribution functions to any…

Statistics Theory · Mathematics 2022-02-24 Igor V. Rodionov

We study the asymptotic spectral distribution of the conjugate kernel random matrix $YY^\top$, where $Y= f(WX)$ arises from a two-layer neural network model. We consider the setting where $W$ and $X$ are random rectangular matrices with…

Probability · Mathematics 2026-01-07 Alice Guionnet , Vanessa Piccolo

We provide a new extension of Breiman's Theorem on computing tail probabilities of a product of random variables to a multivariate setting. In particular, we give a complete characterization of regular variation on cones in $[0,\infty)^d$…

Probability · Mathematics 2020-06-09 Bikramjit Das , Vicky Fasen-Hartmann , Claudia Klüppelberg

The paper presents an elaboration of some results on Lin's conditions. A new proof of the fact that if densities of independent random variables $\xi_1$ and $\xi_2$ satisfy Lin's condition, the same is true for their product is presented.…

Probability · Mathematics 2017-07-24 Alexander Il'inskii , Sofiya Ostrovska

We consider two independent q-Gaussian random variables X and Y and a function f chosen in such a way that f(X) and X have the same distribution. For 0 < q < 1 we find that at least the fourth moments of X + Y and f(X) + Y are different. We…

funct-an · Mathematics 2009-10-28 Hans van Leeuwen , Hans Maassen

At high levels, the asymptotic distribution of a stationary, regularly varying Markov chain is conveniently given by its tail process. The latter takes the form of a geometric random walk, the increment distribution depending on the sign of…

Methodology · Statistics 2014-12-11 Holger Drees , Johan Segers , Michał Warchoł